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Darya [45]
3 years ago
14

Angle A is in standard position and terminates in quadrant IV. If sec(A)=4/3, complete the steps to find cot(A).

Mathematics
2 answers:
Molodets [167]3 years ago
7 0

Answer:

First answer is A.

Second answer is: tan.

Third is answer  C. sqrt7/3

Fourth answer is A. -3sqrt7/7

Step-by-step explanation:

Butoxors [25]3 years ago
6 0

Answer:

Part A) Use the identity tan^2(A)+1=sec^2(A)

Part B) cot(A)=-\frac{3\sqrt{7}}{7}

Step-by-step explanation:

we know that

tan^2(A)+1=sec^2(A) ----> by trigonometric identity

we have

sec(A)=\frac{4}{3}

substitute in the expression above

tan^2(A)+1=(\frac{4}{3})^2

solve for tan(A)

tan^2(A)+1=\frac{16}{9}

tan^2(A)=\frac{16}{9}-1

tan^2(A)=\frac{7}{9}

square root both sides

tan(A)=\pm\frac{\sqrt{7}}{3}

Remember that Angle A terminates in quadrant IV

so

The value of tan(A) is negative

tan(A)=-\frac{\sqrt{7}}{3}

<em>Find the value of cot(A)</em>

we know that

cot(A)=\frac{1}{tan(A)} ----> is the reciprocal

therefore

cot(A)=-\frac{3}{\sqrt{7}}

simplify

cot(A)=-\frac{3\sqrt{7}}{7}

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